Relaxing the Constraints on Locally Recoverable Erasure Codes by Finite Field Element Variation

Abstract

To enable the continued scaling of distributed storage, locally recoverable (LRC) erasure codes are necessary to substantially reduce the number of symbols to access for failure recovery. Codes based on parity splitting and generalized integrated interleaved codes are two categories of LRC codes that achieve good tradeoffs on locality, redundancy, and complexity. The parity check and nesting matrices in these codes are modified to improve the complexity and locality. On the other hand, these structural modifications add constraints on the code parameters. This letter proposes to relax the constraints by exploiting different finite field elements, field constructions, and independent entries in the matrices. The computation complexity of finding the maximum allowed values of the parameters has been reduced by orders of magnitudes through taking advantage of isomorphic mapping and conjugacy classes, as well as developing a decomposed searching method. Significant improvements on the applicable code parameters have been achieved for both codes using the proposed schemes.